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To answer this we need to consider a circle of radius r centred at the origin, drawn in the x,y plane. We'll draw a right-angled triangle such that the hypotenuse is the radius, and say that the point whe...

The question asks for integration by parts. Therefore we need to differentiate one variable and integrate the other. First we need to decide which variable is going to be which. Algebra should always be d...

Gradient is change in y divided change in x.As the change shrinks to effectively nothing (as we want to gradient at a point, not between points), we use dy/dx (the derivative of y with respect to x), to w...

y = x + 3x² + 2y = 9We want to make the squared equation have either only x's or only y's, so we substitute y = x + 3 into the equation:x² + 2(x + 3) = 9We need to take out the brack...

Oxbridge personal statements differ from many other universities, in that they are looking for a more academic personal statement. Whilst other universities might be interested in your extra-curricular ac...